Following data were obtained during the thermal decompoistion of sulphuryl chloride at constant volume and `285^(@)C`.
`SO_(2)Cl_(2)(g) rarr SO_(2) + Cl_(2)(g)`
`|{:("Time (s)",0,240,600),("Pressure (torr)",180,244,302):}|`
Show that it is first order reaction.

Explanation

`{:(,SO_(2)Cl_(2)(g), rarr, SO_(2)(g)+, Cl_(2)(g)), ("Initial",180,,0,0),("At time",180-x,,x,x):}`
`P_("total") = 180 x + x + x = 180 + x`
(a) `t = 240 s, P_(t) = 244`
`:. 180+x = 244 rArr x = 64`
`k = (2.303)/(240)log.(a)/(a-x)`
`= (2.303)/(240) log.(180)/(180-64)`
`= (2.303)/(240) xx 0.1909 = 0.00183 s^(-1)`
(b) `t = 600 s`, `P_(t) = 302`
`180 + x = 302`, `x = 122 "torr"`
`k = (2.303)/(600) log.(180)/(180-122)`
`= (2.303)/(600) xx 0.4918 = 0.0018 s^(-1)`
Since the value of `k` is constant and hence first order reaction.